Path for camera from motion equation
Add a single key frame to the camera the go to the f-curve editor. Selcet the curve for the desired coordinate. Go to the proverties panel of the f-curve editor (if you don't have it press N to get it)

Add a Built-In Function modifier



You're looking for a "sin" type for each of your coeficients.
For example I'll do the X location formula you provided:



Remember to check the "additive" option if your have more then one term in your equation
To enter "cos" you need to use the fact that cos(x)=sin(x+pi/2) Wikipedia: Trigonometric identities

Final graph for X location:



Extension:

In your case you only needed sines and cosines, but it it would be nice if we could do it for any function. It would be nice if we had a any function modifier, but for now heres a work around:
This method is inspired by @gandalf3 comment

Add a driver to the property you want to control using a equation


Then head over to the graph editor, and change from the f-curve editor to the driver-editor. Select the property you want to add an equation to on the left hand side. Now head over the the properties panel. 

There change the variable type to "single property" and select the current scene object (You must first select a scene object type). Then type in "frame_current" into the path box. If you want you can name your variable (I called mine "t")


Now all you need to do is enter your equation into the box "Expr:" Remember that this is a python expresion so a quadratic function is x**2 not x^2



If you get an error saying somthing about "Python Auto-execution disabled: reference this question.